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The first observations of deuterium and oxygen in the Local InterstellarMedium (LISM) obtained with the Far Ultraviolet Spectroscopic Explorer (FUSE)can be used to search for local abundance variations. While the very limitedsample of these first data may be consistent with no variations, they do offera hint of anti-correlated variations between D/H and O/H. If confirmed by moredata (which will require independently determined, accurate HI columndensities), these hints suggest that observations of interstellar gas within afew kpc of the solar neighborhood will reveal clear signs of the evolution ofthe abundance of deuterium from there and then (the Big Bang), to here and now(the Local Interstellar Medium of the Galaxy).Comment: 21 pages, 9 figures, 5 equations, matches final version (minor  changes) to appear in ApJ, v586, n2, April 1, 200

On the Variation of Deuterium and Oxygen Abundances in the Local Interstellar Medium